Question

At the Long-baseline Interferometer Gravitational-wave Observatory (LIGO) facilities in Hanford, Washington, and Livingston, Louisiana, laser beams of wavelength 550.0 nm travel along perpendicular paths 4.000 km long. Each beam is reflected along its path and back 296 times before the beams are combined and compared. If a gravitational wave increases the length of one path and decreases the other, each by 1.000 parts in 1021, what is the resulting phase difference between the two beams

Answer 1

The optical path difference is in each path

$OPD=\frac{2}{1021}L=7.83km$

where L=4000km, so that the total opd is

$OPD_{tot}=nOPD=2319.2km$

and the fase shift is

$\phi=\frac{2\pi}{\lambda}OPD_{tot}=2.7\cdot 10^{16}rad$